# Commuting fraction equals five-eighths iff inner automorphism group is Klein four-group

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## Statement

The following are equivalent for a finite group :

- The Commuting fraction (?) of is exactly equal to .
- The Inner automorphism group (?) of has order equal to four.
- The Inner automorphism group (?) of is a Klein four-group.

The condition defines a family of isoclinic groups. The groups in this family that are 2-groups form the family in the Hall-Senior nomenclature.